Aman travels from town x to town y at an average rate of 60 mph and returns at an average rate of 50 mph. he takes a 1/2 hour longer than he would take if he made the round trip at an average of 55 mph. what is the distance from town x to town y?

Distance = d miles ; rate = 60 mph ; time = d/60 hrs

distance = d miles ; rate = 50 mph ; time = d/50 hrs

Round-trip DATA:
distance = 2d miles ; rate = 55 mph ; time = (2d)/55 hrs

Equation:

Roundtrip time - other time = -1/2 hr
(2d)/55 - [(d/60)+(d/50)] = -1/2
(2d)/55 - [(110d)/(50*60)] = -1/2
---
600(2d) - 11[110d] = -16500
1200d - 1210d = -16500
-10d = -16500
distance = 1650 miles

Hope this helped :)

I’m not absolutely sure but i think it’s 7x6x5x4x3x2=5040 because as the first character you can take any of the 7 given then you are left with 5 then 6 then 4 etc.